An Investigation Of The Use Of Paper Folding Manipulative Material On Learners Performance In Fractions In Grade 9

International Journal of Research and Review
Vol.7; Issue: 8; August 2020
Website: www.ijrrjournal.com
Research Paper E-ISSN: 2349-9788; P-ISSN: 2454-2237
International Journal of Research and Review (ijrrjournal.com) 153
An Investigation of the Use of Paper Folding
Manipulative Material on Learners’ Performance in
Fractions in Grade 9
George Adom, E.O. Adu
Faculty of Education, University of Fort Hare, South Africa.
Corresponding Author: George Adom
ABSTRACT
The aim of this study was to investigate the use
of Paper folding on grade 9 learners’
performance in fractions. Pre-test, Post-test, and
Control group quasi-experimental design was
used to collect data. The study group was made
up of 250 grade 9 learners’ which encompassed
125 learners in the experimental group and 125
learners’ in the control group. Multiple sampling
techniques of systematic simple random,
convenience, purposive and stratified sampling
methods were adopted for the study. The data
collected were analysed using Analysis of
Covariance (ANCOVA) to find the Mean,
Standard Deviation and Sample T-test. The
mean and standard deviation were used to
compare the pre-test and post-test between the
Experimental group and Control group. The
analysed results of the means, standard
deviations and T-tests were used to reject the
null hypotheses. The analysed results of Paper
folding showed that the pre-test (mean = 8.372,
SD=1.770), post-test (mean = 11,792,
SD=4.256), t=12,024 p< 0.05. The hypotheses
were tested at 0.05 level of significance.
Keywords: Educators, Fractions, Grade 9,
Learners’, Manipulative material, Paper folding,
I. INTRODUCTION
Fractions are essential aspect of
mathematics that formed the bedrock of
every learner’s success in mathematics as
postulated by the National Mathematics
Advisory Panel (NMAP, 2008). Lortie-
Forgues, Tian and Siegler (2015) argued
that, the prominence of fractions and
decimal calculation for academic
accomplishment was not restricted to
mathematics courses only. Rational number
arithmetic was also ever-present in physics,
chemistry, engineering, psychology,
sociology, biology, economics, and other
spheres of studies.
Gould, Outhred, and Mitchelmore
(2006), asserted that educators, learners and
academics have typically described fractions
learning as a difficult aspect of mathematics
syllabus. Researchers underscored the fact
that learners found it problematic to
comprehend the idea of “a part as a whole”
relationship in mathematics. Studies showed
that fractions were very challenging topics
educators and learners are confronted with
on daily basis (Tobias, 2013). Most
educators have little knowledge of fractions
necessary for classroom instructions
(Harvey, 2012). The Centre for
Development and Enterprise (CDE, 2011),
indicated that South African learners’ poor
performance in national assessments in
mathematics could be linked to teacher’s
poor content knowledge and lacked of
innovative methods of fractions instructions.
In support, Davis (2016) concurred that
there existed a gap between the way learners
experienced fractions in the out-of-school
and in-school settings. The school
mathematics curriculum had not made the
concepts fractions relevant to learners in
their everyday life activities. Sharing which
formed the basis of the introduction of
fractions as division in schools, was also
widely practiced in the out of school

George Adom et.al. An investigation of the use of paper folding manipulative material on learners’ performance
in fractions in grade 9
environment. It was evident that learners
lacked the knowledge of linking the concept
of fractions at home to the concept of
fractions at school due to the physical
properties that were used in the instructions
(Davis, 2016).
In 2013, the National Council of
Supervisors of Mathematics (NCSM) issued
a position statement on the use of
manipulative concrete materials in
classroom teaching to develop learners’
accomplishment in mathematics. “In order
to develop every student’s mathematical
proficiency, leaders and educators must
systematically integrate the use of concrete
and virtual manipulative into classroom
instruction at all grade levels” (NCSM,
2013). In a similar vein, the West African
Examinations Council (WAEC, 2007) Chief
Examiners report recommended the use of
hands-on and physical illustration in
teaching abstract ideas to enhance
understanding and to awaken and facilitate
learners’ interest in fractions. Van de Walle,
Karp, and Bay (2013), described a
manipulative concrete material as a
mathematical tool or, any item, image, or
drawing that embodied an idea or onto
which the connection for that concept cold
be enacted. In a similar view, manipulative
concrete materials were physical objects
that could be utilized to demonstrate and
undraped mathematical ideas such as
fractions.
Fractions played a very important
role in our technological world because our
daily lives heavily relayed on the ability to
compute fractions correctly, competently,
and insightfully (Pienaar, 2014). Also,
fractions formed the fundamental blocks for
future success in mathematics (National
Mathematics Advisory Panel (NMAP),
2008).
II. LITERATURE REVIEW
Paper manipulative concrete
materials were mathematical tools made
from papers mostly hard cards. They were
made in different shapes, size and colour.
They included; paper folding, puzzles,
hundred charts etc. (Special connection,
2009).
Fig1: Paper manipulative concrete materials. (Source: Ervin 2017).
Fraction could be modelled using a
piece of paper as the physical object to
demonstrate area as fraction multiplication
using paper folding. This demonstration was
generated by folding a piece of paper into
equal sizes in relation to the problem under
study (Ervin, 2017:265). Paper folding
played a very vital role in learners’
comprehension of division in fractions
(Johanning & Mamer, 2014). Through paper
folding modelling, learners were able to
visualised problems in figurative form
through lens that highlighted the scale of the
dividend and divisor. This enabled learners

to make better judgement of their solutions
(Ervin, 2017:265). Frasher (2013), asserted
that learners of all categories of age group
could benefit from the use of concrete
manipulative materials in the instruction of
mathematical concepts. However, Ross
(2008) attested to the fact that educators
who are not in tuned with the applications of
concrete manipulative materials especially
Paper folding are most liable of limiting the
success of teaching, classroom organisation,
and improving learners mathematical
achievements in fractions.
Figure 2 illustrated Paper folding approach
in solving fraction division problem. For
example; solve 3⁄5 ÷ 1⁄3
Fig. 2: Paper folding showing division of fractions (Source: Ervin 2017).
How many 1⁄3 fits into3⁄5? Five grey
blocks made up 1⁄3 of the whole unit. One
whole set of these grey blocks and four out
of five of a second set of grey blocks would
fit into the purple region if we considered
the purple region to contain nine grey
blocks. Thus 3⁄5 ÷ 1⁄3 = 14/5 (Ervin, 2017).
III. Theoretical framework
In this study the researcher adopted
Cognitive Development Theory and
Constructivism Theory for the study.
1. Cognitive development theory:
Cognitive development theory was the
process of receiving information through the
senses as well as the clarification of the
information (Donald et. al., 2010:58;
Robinson & Lomofsky, 2010:34). De Witt
(2011) defined Cognitive development as
the ability to make intellectual judgement
through the process of involving all the
mental faculties to learn, pay attention,
recall, verbalize, make meaningful
discernment, innovation and ingenuity. In a
similar vein, researchers argued that
cognitive development was the ability of
modifying mental capabilities or skills, such
as; language, learning, thinking, attention,
creativity, and reasoning (Lerner & Johns,
2009:153; Papalia, Wendkosolds & Duskin
2008:10). The development of intellectual
abilities and skills were very much
important in solving problems, making
effective decisions and transforming
passive, dependent learners into dynamic
enthusiastic learners who could apply their
cognitive ability into an extensive range of
real life situation (Donald et al., 2010:58;
Eggen & Kauchak, 2010:30; Benjamin,
2009; Lerner & Johns, 2009:164).
2. Constructivist theory:
Constructivist theory dealt with knowledge
acquisition through which individuals

gained information and comprehended the
information from their personal
experienced. In constructivism, entities
developed independent meanings of their
experienced and meanings directed towards
specific items. These items were diverse and
multifaceted, leading the investigator to
look for varied views rather than limiting
understanding into a few categories or
thoughts (Creswell, 2013:8). The significant
aspect of this theory was the decomposition
of each mathematical concept into
developmental phase in line with Piagetian
theory of intellectual development based on
observation and interviews with students as
they tried to learn a concept (Mathforum,
2015). Robson, (2006:13-14); Fraser,
(2013); Troutman and Lichtenberg, (2003),
asserted that the constructivist technique of
tuition identified the significance of the
learner in the learning process and allowed
the learners to discover their own
knowledge through the self-discovery
method.
IV. METHODOLOGY
Multiple sampling techniques of
convenience, purposive and stratified
sampling methods were used to select 40
public schools from Chris Hani West
education district. A sample of 250
participants was selected from the schools
chosen for the study. A systematic simple
random method was used to group 250
participants into Experimental group (125)
and Control group (125). Pre-test and Post-
test were used to collect data from the
Control group and Experimental group.
The null hypothesis was tested at 0.05 level
of significant. The null hypotheses were
stated as followed:
H01: There is no difference between the
results of the Pre-test and Post-test of the
Control group and
Experimental group in Paper folding.
H02: There is no significance influence of
Paper folding on learners’ performance in
fractions in grade
Nine.
V. Data Analysis
H01: There is no difference between the
results of the Pre-test and Post-test of the
Control group and
Experimental group in Paper folding.
Table 1: Findings of Paper Folding Manipulative Tool Data Set
Group N Trial Mean Standard deviation Min Max
Control 125 Pre-test 8.192 1.735 0 14
125 Post-test 7.872 1.465 5 11
Experiment 125 Pre-test 8.552 1.794 2 11
125 Post-test 15.712 1.804 6 19
Source: Field work (February, 2019).
Table 1, illustrated the Mean scores and Standard deviation of the Paper folding
manipulative tool in the Pre-test and Post-test of both Experimental group and Control group.
The Pre-test mean scores and standard deviation of Experimental group (mean = 8.552,
SD=1.794) and Control group (mean = 8.192, SD=1.735) respectively. The Post-test mean
scores and standard deviation showed Experimental group (mean = 15.712, SD= 1.804) and
Control group (mean =7.872, SD=1.465) respectively. The results showed that there is
difference between the results of the Experimental group and Control group in the pre-test
and post-test (P < 0.05). Hypothesis (H01) was therefore rejected.
H02: There is no significance influence of Paper folding on grade nine learners’ performance
in fractions.
Table 2: Analysed results of Paper folding
Pair Mean Std. Deviation Std. Error Mean
Paper folding manipulative Post-test 11.792 4.256 .269
Pre-test 8.372 1.770 .112

Paired Differences t df Sig.
(2-tailed)
Pair Mean Std. Deviation Std. Error Mean 95% Confidence Interval of the Difference
Lower Upper
Paper folding P
ost-test - Pre-test
3.420 4.426 .280 2.868 3.971 12.219 249 .000
Source: Field work (February, 2019).
To prove that there was a significant
relationship between Paper folding and
learners’ performance in fractions, the pre-
test and post-test mean and standard
deviations scores were compared using
sample paired t-test. Table 2, showed the
scores of mean and standard deviation of
Paper folding in the pre-test (mean
=8.372, SD=1.770) and post-test (mean
=11.792, SD=4.256) respectively. This
indicated that the experimental group gained
higher scores in the post-test. The result of
the sample t-test (t=12,219; p < 0.05). This
indicated that there was a significant
relationship between Paper folding and
grade nine learners performance in
fractions. Thus the null hypothesis (H02)
was rejected.
VI. CONCLUSIONS
The study has revealed that Paper
folding manipulative material has a positive
effect on learners’ performance in fractions.
Johanning and Mamer, (2014) asserted that
Paper folding played a very vital role in
learners’ comprehension of division in
fractions Recommendations. In support,
Ervin, (2017) opined that through paper
folding modelling learners were able to
visualise problems in figurative form
through lens that highlighted the scale of the
dividend and divisor and were able to make
better judgement whether their solutions
were viable or not. Ervin (2017:),
emphasised that it was very necessary for
pre-service educators to be able to sketch
and fold area models since paper folding
exposed pupils to physical experience.
The following recommendations were made
from the study:
1. Learners’ ought to use Paper folding
manipulative concrete materials
frequently in their mathematical lessons
so that they would be up-to-date with it
and also increased their comprehension
in fractions.
2. Mathematics educators ought to ensure
that they incorporate Paper folding
manipulative concrete materials in the
instructions of fractions in mathematics.
3. School principals ought to ensure that
mathematics educators integrate Paper
folding manipulative concrete materials
in the instructions of mathematics in
their schools.
4. It should be obligatory for the
Department of Education to ensure that
every school is well resourced with
manipulative concrete materials to
enhance the mathematical proficiency of
the learners’.
5. The government ought to enact policies
that would strictly involve the use of
Paper folding manipulative concrete
materials in the instructions of
mathematics at all grade level.
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How to cite this article: Adom G, Adu EO. An
investigation of the use of paper folding
manipulative material on learners’ performance
in fractions in grade 9. International Journal of
Research and Review. 2020; 7(8): 153-158.
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